David Marjanovic wrote some pointed comments on Gillooly et al. I'd
like to expand on those. Toby White of Palaeos read over a draft of
this post and helped me to clarify it. My comments are my own. however.

The paper by Gillooly et al. offends me deeply. I think it’s very
poor science, so this is an unrepentantly critical comment. I know
that they are innovative, highly regarded hot shots in quantitative
physiology and ecology, but that doesn’t mean that everything they do
is right.

The data come from two sources. The first is a data set from Frank
Seebacher, of crocodile body temperatures measured at various growth
stages of the Australian salt-water crocodile C. porosus. The second
data set consists of curves fitted through estimates of body mass
versus age in nine dinosaurs compiled mainly by Erickson and
colleagues, from which one can read off (estimates of) body mass and
(estimates of) growth rate at various times during growth.

Gillooly et al. have previously arrived at theoretical equations that
(in theory) allow them to estimate body temperature from body mass
and growth rate, based on extant animals over a huge range of sizes.
In particular, they have one equation (one equation to bind them all)
that they seem to regard as universal.

G = g0 . M exp 0.75 . e exp 0.1T

G is maximum growth rate; g0 is a constant; M is body mass, and the
exponent 0.75 is found in a lot of theoretical physiology; T is
temperature, and as in many heat systems, e to the exponent kT is
often seen. In this case, k is 0.1.

They re-arrange this magic equation so that they can read off body
temperature

T = 10 log [G (M exp -0.75)/g0]

Now comes the data processing. The crocodile data contain body mass
and body temperatures for eleven individuals of various sizes.
Plotting log body mass against body temperature, the data fall on
roughly a straight line, showing increasing body temperature with
increasing mass. (There’s a good biological reason for that, as
Seebacher explains in his paper that contains the original data set.
Adult crocs like to thermoregulate behaviorally at temperatures
higher then ambient, and their large body size helps them to do that.
Young crocodiles can’t thermoregulate as well as older ones because
of their smaller body mass, so their body temperatures average at
closer to the ambient Queensland 25° or so.) So no surprises yet,
though note that there are NO data on the growth rates of these
crocodiles.

Gillooly et al. now plot nine dinosaur species on the same axes. This
time, there are no *data* on body temperature, only the estimates
that come from the magic equation. (Actually, there are no *data* on
body mass either: there are estimates, read off the fitted sigmoid
curves published by Erickson et al. 2001, and based on “developmental
mass extrapolation”, a “principle” described by Erickson and Tumanova
2000.) The only data on dinosaur body masses that Erickson et al.
regard as valid are those for final adult mass. This adult mass
provides the asymptotic maximum weight that helps to define the
sigmoid growth curve that Erickson et al. chose to model their
dinosaurs.

Gillooly et al. further chose to use only one “data point” for each
dinosaur: the (inferred) body mass at precisely half the (estimated)
final adult size; and the maximum growth rate reached during ontogeny
(measured by Erickson et al. on bone growth rings on long bones, and
then converted by them into mass per day in a process that involved
using the (inferred interpolated) half-size body mass.

Using this one “data point” for mass and maximum growth rate,
Gillooly et al. calculate body temperature from the equation above.

Well, OK, it’s at the end of a long chain of reasoning, but what do
you do with these nine calculated body temperatures?

Gillooly et al. plotted the nine points on the same plot with the
crocodile data, in their Figure 1. The two data sets are not
congruent, as explained above, so this may not really be legitimate.
Then the first thing Gillooly et al. did was to throw away two of the
nine data points (they didn’t meet expectations). They threw out the
data point from Syntarsus because it “is clearly an outlier, and is
therefore excluded from subsequent analyses”. Can you believe that?
You could clean up all kinds of data sets using that logic! I suspect
that the real problem with the Syntarsus data, from their point of
view, is that it showed up as warm-blooded and small! They also threw
out the data from “the dinosaur bird” (sic!) Shuvuuia “because it is
a feathered species and is therefore fundamentally different than the
eight more reptile-like species” that remained in the data pool.
Again, I suspect that the real problem with the Shuvuuia data, from
their point of view, is that it showed up as warm-blooded and small!

If you look at their Figure 1, you notice that once Shuvuuia and
Syntarsus are removed, five of the “data points” from the seven
remaining dinosaurs, from 20 kg adult size to 2000 kg adult size, lie
close to the crocodile data, with inferred maximum body temperatures
around 25°C. However, the remaining two dinosaurs are clearly
outliers too: Tyrannosaurus and Apatosaurus. Instead of excluding
them, Gillooly et al. point to them and rely on them for their most
outrageous inferences. Tyrannosaurus is inferred to have had a body
temperature around 33-34°C (not unreasonable), while Apatosaurus is
estimated at 41-42°C (quite unreasonable). Schmidt-Nielsen years ago
pointed out that most animals leave a safety margin of about 6°
between their preferred maximum body temperature and the temperature
that kills them. The inferred level for Apatosaurus puts it into the
lethally challenged level, yet Gillooly et al. cheerfully extrapolate
again, even without any inference on growth rate, to arrive at a body
temperature of 48° C for the giant sauropod Sauroposeidon.

But we are not yet done. Because their equation predicts that body
temperature increases with body mass, Gillooly et al. are led to the
conclusion that growing dinosaurs would change their body temperatues
with growth. And that change would have been dramatic if the equation
is correct. For example, the body temperature of an Apatosaurus would
increase by more than 20°C during ontogeny. This is physiologically
and biochemically outrageous. Many biochemical molecules are strongly
temperature-dependent, and it is vanishingly unlikely that a growing
Apatosaurus could overhaul its basic biochemistry within a few years.
This is a very different situation from that of a tropical crocodile
changing its preferred temperature by 5° or less.

I wonder what happens in adults that have reached their final adult
size (and thus have a growth rate close to zero. Using the same logic
and the same equation that Gillooly et al. use to “calculate”
temperature during ontogeny, I calculate that the body temperature of
an adult Apatosaurus is close to zero [Kelvin].

So what went wrong? I think that Gillooly et al. assumed from the
beginning that dinosaurs were poikilothermic, and every time they had
to make a decision about data processing or interpretation, they made
a decision that helped to fulfil their expectation.

Suppose we plot body temperature, body mass, and growth rate in a
group of dominant terrestrial animals of today: the mammals. We
gather data from mammals from bats to blue whales (a larger range of
body mass than dinosaurs can boast). We find that growth rate is
independent of body temperature, and that body mass is independent of
body temperature. If we then ask whether the dinosaur data in any way
invalidates the idea that dinosaurs were homeothermic, the answer
would be no. In other words, we would have tested the homeothermic
hypothesis, and failed to falsify it.

And the same principle would apply to living birds, from hummingbirds
to ostriches.

So how about the analysis by Gillooly et al.? They used the
assumption that dinosaurs were “reptile-like” (that’s the word they
used in their paper). They threw out data points that they decided
were anomalous outliers, or which came from feathered dinosaurs
(“dinosaur birds”). Their culled dinosaur “data” (actually, a
compendium of inference and estimate) looked like the crocodile data,
but only over the body size range of crocodiles. Their inferences
about dinosaur physiology, especially the ontogenetic range of body
temperature in large dinosaurs, are biologically unreasonable. Any
reasonable observer would conclude that their tacit hypothesis of
poikilothermy in dinosaurs has been falsified.

There should be an award for authors who inadvertently destroy the
hypothesis they are pushing.

And what about the review process? Is this a case of “Publish them
all, and let God sort them out!”?

BACKGROUNDER ON THE RESEARCH PROGRAM of GILLOOLY et al.(open access)
See 2005 Science News article at www.sciencenews.org/articles/
20050212/bob9.asp